Question

Solve for x: (x+a)+1/(x+a)=c+1/c

Answer 1

Answer:

$solve\:for\:x,\:\left(x+a\right)+\frac{1}{\left(x+a\right)}=c+\frac{1}{c}\quad :\quad x=c-a,\:x=\frac{-ac+1}{c};\quad \:c\ne \:0$

Step-by-step explanation:

$\left(x+a\right)+\frac{1}{\left(x+a\right)}=c+\frac{1}{c}$

$\left(x+a\right)+\frac{1}{x+a}=c+\frac{1}{c}$

$\left(x+a\right)c\left(x+a\right)+\frac{1}{x+a}c\left(x+a\right)=cc\left(x+a\right)+\frac{1}{c}c\left(x+a\right)$

$c\left(x+a\right)^2+c=c^2\left(x+a\right)+x+a$

$x=c-a,\:x=\frac{-ac+1}{c};\quad \:c\ne \:0$